SOLUTION: please help me with this problem.. in 2005 consumers received an average of 3253 spam messages.the volume of spam messages is decreasing with an exponential decay rate of 13.7% pe

Question 270747: please help me with this problem..
in 2005 consumers received an average of 3253 spam messages.the volume of spam messages is decreasing with an exponential decay rate of 13.7% per year.
a--find th eexponential decay function that can be used to predict average number of spam messages m(t)+years after 2005.
b--predict the number of spam messagesreceived per consumer in 2010.
c--in what year will the average consumer receive 100 spam messages?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
please help me with this problem..
in 2005 consumers received an average of 3253 spam messages.the volume of spam messages is decreasing with an exponential decay rate of 13.7% per year.
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If the decay rate is 13.7%, the survival rate is 86.3%
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a--find th exponential decay function that can be used to predict average number of spam messages m(t)+years after 2005.
A(t) = 3253(0.863)^t where t is the number of years after 2005
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b--predict the number of spam messages received per consumer in 2010.
A(5) = 3253(0.863)^5 = 1557.18
Rounding up get A(5) is approximately 1558
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c--in what year will the average consumer receive 100 spam messages?
Solve for "t":
100 = 3253(0.863)^t
0.863^t = 0.06418
t = log(0.06418)/log(0.863) = 18.64 yrs
Round up: t = 19 yrs.
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Cheers,
Stan H.
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